Per-Gunnar Martinsson
Department of Mathematics, Yale University
In this talk, I will discuss methods for numerically solving linear boundary value problems. I will start by describing a set of iterative methods for such problems that in many situations are very fast and accurate. I will then describe a recently developed procedure that solves the equations directly. This is a more robust procedure that in some important environments significantly outperforms earlier iterative methods, and in others allow the solution of problems that had previously been considered unsolvable. The impact of this work on fields such as electro-magnetic scattering, modelling of macro-molecules, and numerical linear algebra will be discussed and illustrated with computational examples.